This invention relates to a method and apparatus for measuring the Fourier transform of a spatially recorded pattern derived from a time varying signal or waveform. More specifically, it relates to the application of certain phenomena and relationships of optics to generate the Fourier transform spectrum for an input transmittance record and the application of certain phenomena and relationships of electronics to generate the magnitude and phase components of the transform spectrum.
Signal processing with very high spectral resolution, or equivalently large time bandwidth product, coupled with a multichannel format is of value in several important areas. For example, in radar applications, improved signal frequency resolution for FM or Doppler radars results in an enhanced range resolution capability since range resolution is determined by signal frequency resolution. Better frequency resolution also aids discrimination of multiple targets whose Doppler frequencies are relatively close, corresponding to small differences in target speeds. Sensitive Doppler frequency discrimination is also needed to increase the target to clutter ratio in a moving target indicator radar (MTI). Large time bandwidth systems are also useful in wideband RF signal processing, EM spectrum surveillance, acoustic signal processing, speech analysis applications, and signal correlators.
Fourier spectrum analysis of time varying signals by means of light diffraction is an inherent property of coherent optical processors responsible for continued interest in optical analog methods. Several types of processing systems have evolved for applications dealing with signal power spectrum analysis and correlation.
The so-called space integrating technique involves processing a temporal signal recorded as a transmittance pattern in a two- dimensional raster format. This type of processor offers extremely high resolution (or time bandwidth product) analysis of isolated, pure tone frequencies. With appropriate precautions, the power spectral density of signals with continuous spectra can also be obtained.
A second class, called time integrating processors, requires no spatial signal storage prior to processing. Instead, one relies upon temporal integration of intensity modulated beams with an output detector.
Several acoustooptic systems have been proposed to take advantage of some desirable features from each of the above mentioned methods. Both techniques require the use of several acoustooptic modulators for temporal signal modulation and for chirp waveform phase modulation as well. Two dimensional interrogation of an output plane would still be used for coarse and fine frequency display of an isolated, pure tone input signal. The output scanning format needed for high resolution performance is still complicated for signals with continuous spectra.
There are several major limitations to these presently used techniques. In these conventional optical Fourier processors, the length or time duration of the signal to be Fourier analyzed is set by the size of the aperture or the time constant of the detection and associated circuitry. Signals that extend beyond the aperture or are longer in time than the time constant factors cannot be processed coherently; that is, the resolution of the spectrum is established by these limiting system constraints. Also, the output of these systems deals with a light intensity pattern that is proportional to the power spectral density (PSD) of the signal to be analyzed and not its Fourier transform.
A two dimensional system can achieve high resolution analysis with restrictions. However, the ability to process simultaneously more than one signal is lost with such systems. Two dimensional Fourier processors can only yield high resolution spectral analysis when the output light pattern is scanned or interrogated in a very special manner. To achieve high resolution, one must scan the output distribution in a complicated, raster-like fashion. In addition, the output is proportional to the signal PSD and not its Fourier transform components. Also, certain time-integrating optical processors need more than one acoustooptic modulator.
An optimal Fourier transform signal processor would have several important attributes. In particular, it should be capable of providing high spectral resolution. Moreover, it should be capable of multichannel operation. Also, it should not be limited to signal PSD measurements alone. Instead, it should be capable of providing the more fundamental signal Fourier transform magnitude and phase components, (with which one can then perform correlation, convolution, frequency band analysis as well as PSD operations). It should not be limited to signals with narrow band frequency content, but should be able to process signals with continuous spectral features as well.
It is accordingly a general object of the present invention to overcome the aforementioned limitations and drawbacks associated with the known processors and to fulfill the needs mentioned by providing a method and apparatus for Fourier Transform measurements of temporal signals having characteristics more nearly approaching the optimal attributes noted above.
It is a specific object of the present invention to provide a method and apparatus for measuring the Fourier transform of a spatially recorded pattern derived from a time varying signal or waveform with very high resolution.
Other objects will be apparent in the following detailed description and practice of the invention.